Promoting Geometric Thinking in Grade Four

Date of Completion

5-31-1993

Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson

Abstract

The purpose of this thesis is to describe the development, implementation, and assessment of approaches to geometric teaching and learning which are designed to help children engage in higher levels of mathematical thinking. Although focused on fourth grade, the thesis is broad enough to provide classroom teachers across the grades and supervisors of elementary mathematics with ideas and examples to be used as points of departure for the infusion of higher order thinking within their mathematics classrooms. After reviewing the historical content of mathematical achievement in the United States from the late l870's to l990, the thesis presents relevant research findings of educators and cognitive psychologists, as well as the recent recommendations and the guidelines of the National Council of Teachers of Mathematics. Such research describes how instruction in mathematics generally, and in geometry specifically, can be changed to promote better mathematical thinking among students and teachers. A collection of geometry lessons informed by the research and designed to encourage higher order thinking and mathematical insight are described and analyzed. The geometry lessons are selected from a year-long fourth grade geometry program comprised of two major units; Pentominoes, and Plygons and Tessellations. An authentic assessment method is employed to evaluate student learning throughout the units. This multi dimensional approach to assessment is designed to both document and promote geometric thinking. This approach to assessment includes portfolios comprised of a rich collection of student work and reflections. The portfolios include completed assignments, journal entries, plans, designs, and projects. Students' exhibitions are employed as part of the assessment method. These presentations of long-term investigations are focused on student projects as evidence of problem-solving. Although the intervention described in this thesis, the development and implementation of instruction, and assessment methods to promote geometric thinking met with a fair amount of success, the following areas are recommended for future emphasis: teaching of thinking skills, development of materials, cooperative learning, students' reflections, students' attitudes and approaches to learning, and students' exhibitions of learning.

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